1 Introduction

2 Data

2.1 Data structure

Total 1947 community timeseries we have collected for the timespan 1979-2019. 4 taxa are considered - birds, fish, freshwater invertebrates, terrestrial invertebrates. Below is the summary of the datatable. Description of each column is given in README.txt

## 'data.frame':    1947 obs. of  63 variables:
##  $ source                  : chr  "BioTIME" "BioTIME" "BioTIME" "BioTIME" ...
##  $ STUDY_ID                : chr  "57" "229" "229" "229" ...
##  $ newsite                 : chr  "57" "STUDY_ID_229_LAT35.04016_LON-83.36127" "STUDY_ID_229_LAT35.11187_LON-83.39091" "STUDY_ID_229_LAT35.14137_LON-83.29577" ...
##  $ REALM                   : chr  "Freshwater" "Freshwater" "Freshwater" "Freshwater" ...
##  $ TAXA                    : chr  "fish" "fish" "fish" "fish" ...
##  $ ORGANISMS               : chr  "fish" "fish" "fish" "fish" ...
##  $ initR                   : int  76 24 30 32 25 37 22 30 26 31 ...
##  $ nsp                     : int  34 14 11 17 14 16 13 11 14 10 ...
##  $ nyr_used                : int  32 23 20 21 21 23 23 20 20 28 ...
##  $ startyr                 : int  1981 1990 1990 1991 1990 1990 1990 1995 1995 1979 ...
##  $ endyr                   : int  2012 2013 2013 2012 2013 2013 2013 2014 2014 2006 ...
##  $ nint                    : int  561 91 55 136 91 120 78 55 91 45 ...
##  $ nind                    : int  503 59 35 97 61 91 67 46 60 36 ...
##  $ npos                    : int  35 29 20 27 29 27 11 7 26 7 ...
##  $ nL                      : int  24 21 13 9 3 14 3 3 15 7 ...
##  $ nU                      : int  11 8 7 18 26 13 8 4 11 0 ...
##  $ nneg                    : int  23 3 0 12 1 2 0 2 5 2 ...
##  $ L                       : num  3.027 2.557 1.046 1.028 0.267 ...
##  $ U                       : num  -1.252 -0.633 -0.49 -2.547 -2.938 ...
##  $ f_nind                  : num  0.897 0.648 0.636 0.713 0.67 ...
##  $ f_nL                    : num  0.0428 0.2308 0.2364 0.0662 0.033 ...
##  $ f_nU                    : num  0.0196 0.0879 0.1273 0.1324 0.2857 ...
##  $ f_nneg                  : num  0.041 0.033 0 0.0882 0.011 ...
##  $ cvsq_real               : num  1.565 0.189 0.239 0.11 0.158 ...
##  $ cvsq_indep              : num  1.5001 0.0963 0.0879 0.0475 0.1099 ...
##  $ phi                     : num  1.04 1.96 2.72 2.33 1.44 ...
##  $ phi_LdM                 : num  0.454 0.552 0.388 0.442 0.542 ...
##  $ skw_real                : num  5.172 0.363 0.505 2.41 -0.296 ...
##  $ skw_indep               : num  5.064 0.612 0.737 0.841 -0.877 ...
##  $ phi_skw                 : num  1.021 0.593 0.685 2.866 0.337 ...
##  $ iCV                     : num  0.799 2.303 2.045 3.008 2.512 ...
##  $ iCValt                  : num  1.81 1.9 1.56 3.7 2.15 ...
##  $ LONGITUDE               : num  -89.5 -83.4 -83.4 -83.3 -83.5 ...
##  $ LATITUDE                : num  44 35 35.1 35.1 35.2 ...
##  $ t_med                   : num  2809 2865 2868 2864 2864 ...
##  $ t_skw                   : num  0.4478 0.1228 0.158 -0.0283 0.0353 ...
##  $ t_var                   : num  0.00401 0.00228 0.00208 0.00233 0.00239 ...
##  $ t_kurt                  : num  3.18 2.33 2.27 2.55 2.39 ...
##  $ t_varIQR                : num  11.27 6.54 5.98 6.67 6.83 ...
##  $ t.lm.slope              : num  0.341 0.258 0.106 0.365 0.2 ...
##  $ t.lm.slope.sig          : int  1 0 0 0 0 0 0 0 0 0 ...
##  $ t.sens.slope            : num  0.333 0.333 0.215 0.448 0.319 ...
##  $ t.sens.slope.sig        : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ t_med_celsius           : num  7.77 13.31 13.67 13.23 13.2 ...
##  $ t_skw_celsius           : num  0.4478 0.1228 0.158 -0.0283 0.0353 ...
##  $ is.sig_t_skw_celsius    : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ t_var_celsius           : num  0.145 0.0492 0.0438 0.0504 0.0518 ...
##  $ t_kurt_celsius          : num  NA NA NA NA NA NA NA NA NA NA ...
##  $ is.sig_t_kurt_celsius   : int  NA NA NA NA NA NA NA NA NA NA ...
##  $ t_varIQR_celsius        : num  1.127 0.654 0.598 0.667 0.683 ...
##  $ t.lm.slope.celsius      : num  0.0341 0.0258 0.0106 0.0365 0.02 ...
##  $ t.lm.slope.sig.celsius  : int  1 0 0 0 0 0 0 0 0 0 ...
##  $ t.sens.slope.celsius    : num  0.0333 0.0333 0.0215 0.0448 0.0319 ...
##  $ t.sens.slope.sig.celsius: int  0 0 0 0 0 0 0 0 0 0 ...
##  $ is.stationary.adf       : int  0 1 1 0 1 1 1 1 1 0 ...
##  $ is.trend.stationary.kpss: int  0 0 0 0 0 0 0 0 0 0 ...
##  $ GiniSimpson             : num  0.817 0.57 0.92 0.819 0.521 ...
##  $ Simpson                 : num  0.142 0.152 0.555 0.256 0.138 ...
##  $ Shannon                 : num  0.67 0.512 0.863 0.695 0.471 ...
##  $ Heip                    : num  0.291 0.22 0.693 0.385 0.19 ...
##  $ McIntosh                : num  0.658 0.428 0.852 0.688 0.384 ...
##  $ SmithWilson             : num  0.415 0.35 0.627 0.315 0.325 ...
##  $ Pielou                  : num  0.19 0.194 0.36 0.245 0.178 ...

3 Methods

Temperature timeseries figure with real data

Figure 3.1: Temperature timeseries figure with real data

3.1 Variables estimated and modelled

(Perhaps make this into a table.)

Let \(N_{i,t,s}\) be the abundance (sometimes it was biomass data when abundance data were not available) of species \(i\) at time \(t\) at site \(s\). Total abundance at time \(t\) at site \(s\) is \(N_{t,s} = \sum_{i=1}^{s} N_{t,s,i}\).

Community stability at site \(s\) was estimated as the inverse of the coefficient of temporal variation in total community abundance (when abundance info were not available, then biomass): \(TempStab_s = 1 / CV(N_{t,s}) = abs(mean(N_{t,s})) / sd(N_{t,s})\)

Species richness at site \(s\) was estimated as the number of total species (\(nsp\)) and dominant species that were present minimum 70% of the total years sampled (\(R\)).

Species evenness at site \(s\) was estimated as Smith-Wilson matrix.

Community variance ratio: a measure of synchrony, scaled between 0 to 1 (Loreau & Mazancourt).

Community level total tail association from pairwise synchrony: see BioDyn project, Figure 1.

Temperature median: Median of CHELSA-extracted annual temperature timeseries for the study years included in the analysis for each community.

Temperature trend: Monotonic trend of annual temperature timeseries (computed by non-parametric Sen’s method or parametric linear fit slope). I used the Sen’s slope in the path model, as non-parametric estimation has some advantage, see wikipedia, but it is very similar to linear slope (see 4.24).

Temperature skew: Skewness of CHELSA-extracted annual temperature timeseries for the study years included in the analysis for each community.

Temperature variability: Temperature variability for the community during the study period = IQR(annual temperature distribution for the study period).

4 Results

4.1 Community stability exploration

Stability-diversity relationship for birds and fish.

Figure 4.1: Stability-diversity relationship for birds and fish.

4.1.1 Birds

Stability-diversity relationship for birds at different temperature levels

Figure 4.2: Stability-diversity relationship for birds at different temperature levels

Stability-temperature relationship for bird communities at different richness levels

Figure 4.3: Stability-temperature relationship for bird communities at different richness levels

Stability-synchrony relationship for birds at different temperature levels

Figure 4.4: Stability-synchrony relationship for birds at different temperature levels

Synchrony-temperature relationship (scatterplot)

Figure 4.5: Synchrony-temperature relationship (scatterplot)

Synchrony-temperature relationship (boxplot)

Figure 4.6: Synchrony-temperature relationship (boxplot)

Synchrony richness relationship.

Figure 4.7: Synchrony richness relationship.

Synchrony temperature relationship.

Figure 4.8: Synchrony temperature relationship.

Stability - temperature skew relationship.

Figure 4.9: Stability - temperature skew relationship.

Stability - temperature skew relationship.

Figure 4.10: Stability - temperature skew relationship.

Stability - temperature skew relationship.

Figure 4.11: Stability - temperature skew relationship.

Stability - temperature skew relationship.

Figure 4.12: Stability - temperature skew relationship.

4.1.1.1 Basic statistics for birds

Model of bird stability:

term estimate std.error statistic p.value
(Intercept) 4.3009 0.4507 9.5429 0.0000
nsp 0.0315 0.0107 2.9469 0.0033
t_med_celsius -0.1413 0.0370 -3.8197 0.0001
nsp:t_med_celsius 0.0034 0.0009 3.8206 0.0001

Model of bird synchrony:

term estimate std.error statistic p.value
(Intercept) 0.2954 0.0218 13.5237 0.0000
nsp -0.0027 0.0005 -5.2091 0.0000
t_med_celsius 0.0033 0.0018 1.8185 0.0692
nsp:t_med_celsius -0.0001 0.0000 -1.4679 0.1424

4.1.1.2 Bird conclusions

Bird communities display a positive richness stability relationship. This relationship is stronger at higher temperatures. Equally, high richness bird communities are more stable at higher temperatures, while low richness bird communities are less stable at higher temperatures.

There is some suggestion that this may be explained by synchrony, but the statistics show no strong associations of synchrony with \(t_{med}\).

4.1.2 Fish

Stability-diversity relationship at different temperature levels

Figure 4.13: Stability-diversity relationship at different temperature levels

Stability-temperature relationship at different richness levels

Figure 4.14: Stability-temperature relationship at different richness levels

Stability-synchrony relationship at different temperature levels

Figure 4.15: Stability-synchrony relationship at different temperature levels

Synchrony-temperature relationship (scatterplot)

Figure 4.16: Synchrony-temperature relationship (scatterplot)

Synchrony-temperature relationship (boxplot)

Figure 4.17: Synchrony-temperature relationship (boxplot)

Synchrony richness relationship.

Figure 4.18: Synchrony richness relationship.

Synchrony temperature relationship.

Figure 4.19: Synchrony temperature relationship.

Stability - temperature skew relationship.

Figure 4.20: Stability - temperature skew relationship.

Stability - temperature skew relationship.

Figure 4.21: Stability - temperature skew relationship.

Stability - temperature skew relationship.

Figure 4.22: Stability - temperature skew relationship.

Stability - temperature skew relationship.

Figure 4.23: Stability - temperature skew relationship.

4.1.2.1 Fish basic statistics

Model of fish stability:

term estimate std.error statistic p.value
(Intercept) 0.3925 0.1402 2.7986 0.0053
log2(nsp) 0.0567 0.0797 0.7109 0.4774
t_med_celsius 0.0270 0.0167 1.6152 0.1068
log2(nsp):t_med_celsius -0.0105 0.0078 -1.3434 0.1797

Model of fish synchrony:

term estimate std.error statistic p.value
(Intercept) -0.1910 0.1212 -1.5752 0.1158
log2(nsp) -0.3236 0.0689 -4.6968 0.0000
t_med_celsius -0.0293 0.0144 -2.0267 0.0432
log2(nsp):t_med_celsius 0.0075 0.0068 1.1036 0.2702

4.1.2.2 Fish conclusions

No significant interaction between richness and temperature for fish.

Distribution of temperature trend estimated by non-parametric Sen's slope, and parametric linear fit slope. Colored points are significant Sen's slope (green: birds, blue: fish).

Figure 4.24: Distribution of temperature trend estimated by non-parametric Sen’s slope, and parametric linear fit slope. Colored points are significant Sen’s slope (green: birds, blue: fish).

## 
##  Freshwater Terrestrial 
##   0.3344828   0.2471910
Histogram plot for trends, both taxa.

Figure 4.25: Histogram plot for trends, both taxa.

Histogram plot for variability in temperature

Figure 4.26: Histogram plot for variability in temperature

Histogram plot for variability in temperature

Figure 4.27: Histogram plot for variability in temperature

Histogram plot for variability in temperature

Figure 4.28: Histogram plot for variability in temperature

Histogram plot for variability in temperature

Figure 4.29: Histogram plot for variability in temperature

4.2 Explanations

So, from the exploratory plots we can see: at higher temperature positive stability-diversity relationship becomes stronger for birds but for fish it becomes weaker. Also fish becomes more asynchronous with increasing temperature. So, why does that happen? to find this we could explore how much the bird species and fish species are consistent to temperature change across all communities.

The cue is: if fish species are not much consistent in their response to warming and vary across sites, that means you cannot make a conclusion that they would become similar with changing temperature. On another note, bird species should be more consistent towards warming if their is no change in their synchrony level across communities. Another possibility could be with changing temperature you might loose some species (its not just number of individuals, it will selectively prefer few species with better fitness), and then the communities will be dominated by few species with similar traits (so increasing synchrony). we will test this below.

From the above plots, we can see birds are showing consistent response-distribution across all temperature change, i.e., in either end of temperature spectrum (low or high end). That’s why the synchrony level remains similar for birds. But for fish, warming increases the richness (addition of new species), and as fish species now become more variable in response to temperature sensitivity (trait-variation), they show more asynchrony compared to low temperature scenario where only few species exists (see smaller circle size on the map for lowT,<50%CI) and show similar traits (so more synchrony). Note: when I show this to Frank, he commented on how much robust is the pattern for fish at low T as there are only few species existed across 145 sites - so it also depends on how we considered the lowT-highT communities. I set beyond 50% CI of temperature range as low/high. Even if I decrease that to 30% CI, still very few species found in low T sites (15 sp across 203 sites: 80% >0, 20% <0 line).

To further explore this idea: we collected traits data for birds and fish species used in the analysis. For fish-traits, I will use body length measurements, for bird-traits I will use HWI (Hand-wing index). From below figures: at high T, birds have slightly less dispersal ability (lower HWI), but richness is more or less uniformly spread at either temperature range. For fish, at lowT, few large species exists with similar traits (remember the previous histogram plot 90-10) showing higher synchrony, as temperature increases addition of new small fishes in the community (maybe better environment for them to exist in that temperature rather than too cold water) makes them asynchronous with more trait variation (histogram plot 66-34).

When I showed this to Blake, he was not convinced by the idea to split the data into two: low/high based on t_med (to him this temperature difference is more on latitudinal differences as shown in the map), and same species can exist in both communities - so why changing t_med should change the synchrony level for fish? and getting different bodysize fish from low/high t_med (fewer big fish in lowT and many smaller fish in highT) is not explaining why big fish should be more synchronous - is it because of fewer species (richness) or because bigger fish abundance change needs more time - not on annual scale?

So, I thought to make a plot of how community-level average response traits (average of standardised correlation between species abundance with t_med timeseries across sites) changes with increasing temperature (t_med)? For fish, it should decrease with increasing t_med, whereas for birds it should be a flat relationship.

Possible explanation:

Response variation with temperature

Figure 4.30: Response variation with temperature

Now, we will do a path analysis for a simplistic mixed effect model to see the environmental effects on community stability for both taxa.

## ============ model summary for birds ===========
## # Check for Multicollinearity
## 
## Low Correlation
## 
##                  Term  VIF   VIF 95% CI Increased SE Tolerance Tolerance 95% CI
##                     R 1.88 [1.74, 2.05]         1.37      0.53     [0.49, 0.57]
##                     E 1.10 [1.05, 1.19]         1.05      0.91     [0.84, 0.95]
##                    VR 1.91 [1.77, 2.08]         1.38      0.52     [0.48, 0.57]
##                     A 2.15 [1.98, 2.35]         1.47      0.46     [0.43, 0.50]
##         t_med_celsius 1.14 [1.09, 1.23]         1.07      0.88     [0.81, 0.92]
##  t.sens.slope.celsius 1.07 [1.03, 1.17]         1.04      0.93     [0.85, 0.97]
##         t_skw_celsius 1.03 [1.00, 1.22]         1.01      0.97     [0.82, 1.00]
##      t_varIQR_celsius 1.11 [1.06, 1.20]         1.05      0.90     [0.83, 0.95]
## 
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## 
## Structural Equation Model of psem_birds$model_psem 
## 
## Call:
##   A ~ R + E + VR + MedianT + VarT + TrendT + SkewT
##   VR ~ R + E + MedianT + VarT + TrendT
##   R ~ MedianT + VarT + TrendT
##   E ~ R + MedianT + VarT + TrendT
##   stability ~ R + E + VR + A + (R:MedianT) + MedianT + VarT + TrendT + SkewT
## 
##     AIC
##  13982.614
## 
## ---
## Tests of directed separation:
## 
##     Independ.Claim Test.Type       DF Crit.Value P.Value 
##    R ~ SkewT + ...      coef 1237.784     0.0534  0.8173 
##    E ~ SkewT + ...      coef 1239.821     3.2520  0.0716 
##   VR ~ SkewT + ...      coef  937.269     0.2742  0.6006 
## 
## --
## Global goodness-of-fit:
## 
## Chi-Squared = NA with P-value = NA and on 3 degrees of freedom
## Fisher's C = 6.697 with P-value = 0.35 and on 6 degrees of freedom
## 
## ---
## Coefficients:
## 
##    Response Predictor Estimate Std.Error        DF Crit.Value P.Value
##           A         R   0.7455    0.0222  446.3098  1111.4656  0.0000
##           A         E   0.1624    0.0212  700.9222    57.8476  0.0000
##           A        VR   0.6063    0.0209 1184.5456   839.6357  0.0000
##           A   MedianT  -0.0085    0.0259  164.4514     0.1058  0.7454
##           A      VarT   0.0529    0.0233  700.1938     5.1095  0.0241
##           A    TrendT   0.0173    0.0237  300.5050     0.5238  0.4698
##           A     SkewT  -0.0512    0.0207  442.1973     6.0023  0.0147
##          VR         R  -0.3076    0.0321  832.6035    90.6595  0.0000
##          VR         E  -0.2165    0.0299 1060.2572    52.1107  0.0000
##          VR   MedianT  -0.0022    0.0457  228.2758     0.0023  0.9619
##          VR      VarT  -0.0688    0.0338 1035.7142     4.1150  0.0428
##          VR    TrendT  -0.0335    0.0375  599.1077     0.7868  0.3754
##           R   MedianT  -0.0310    0.0516  693.6981     0.3563  0.5507
##           R      VarT   0.0236    0.0291 1238.6214     0.6521  0.4195
##           R    TrendT  -0.0012    0.0345 1230.3185     0.0011  0.9730
##           E         R  -0.0800    0.0313 1234.0487     6.5225  0.0108
##           E   MedianT   0.1189    0.0549  545.3556     4.6386  0.0317
##           E      VarT   0.0163    0.0322 1240.9500     0.2548  0.6138
##           E    TrendT   0.0834    0.0379 1188.0874     4.8253  0.0282
##   stability         R   0.1308    0.0318 1104.6547    16.7942  0.0000
##   stability         E  -0.0510    0.0225 1094.9592     5.1143  0.0239
##   stability        VR  -0.6950    0.0270 1227.0471   662.4722  0.0000
##   stability         A  -0.1304    0.0275 1220.2194    22.3790  0.0000
##   stability   MedianT  -0.0025    0.0374  265.5627     0.0044  0.9471
##   stability      VarT  -0.0192    0.0245 1001.6151     0.6107  0.4347
##   stability    TrendT   0.0314    0.0277  628.5534     1.2779  0.2587
##   stability     SkewT   0.0116    0.0225  892.4499     0.2633  0.6080
##   stability R:MedianT   0.0423    0.0229  758.5298     3.3823  0.0663
##   Std.Estimate    
##         0.7455 ***
##         0.1624 ***
##         0.6063 ***
##        -0.0085    
##         0.0529   *
##         0.0173    
##        -0.0512   *
##        -0.3076 ***
##        -0.2165 ***
##        -0.0022    
##        -0.0688   *
##        -0.0335    
##        -0.0310    
##         0.0236    
##        -0.0012    
##        -0.0800   *
##         0.1189   *
##         0.0163    
##         0.0834   *
##         0.1308 ***
##        -0.0510   *
##        -0.6950 ***
##        -0.1304 ***
##        -0.0025    
##        -0.0192    
##         0.0314    
##         0.0116    
##         0.0481    
## 
##   Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05
## 
## ---
## Individual R-squared:
## 
##    Response method Marginal Conditional
##           A   none     0.59        0.60
##          VR   none     0.15        0.32
##           R   none     0.00        0.65
##           E   none     0.03        0.57
##   stability   none     0.57        0.65
## ============ model summary for fish ===========
## # Check for Multicollinearity
## 
## Low Correlation
## 
##                  Term  VIF   VIF 95% CI Increased SE Tolerance Tolerance 95% CI
##                     R 3.00 [2.64, 3.44]         1.73      0.33     [0.29, 0.38]
##                     E 1.26 [1.16, 1.42]         1.12      0.79     [0.71, 0.86]
##                    VR 1.30 [1.19, 1.46]         1.14      0.77     [0.69, 0.84]
##                     A 2.42 [2.15, 2.76]         1.56      0.41     [0.36, 0.47]
##         t_med_celsius 1.44 [1.32, 1.62]         1.20      0.69     [0.62, 0.76]
##  t.sens.slope.celsius 1.15 [1.08, 1.30]         1.07      0.87     [0.77, 0.93]
##         t_skw_celsius 1.22 [1.13, 1.37]         1.11      0.82     [0.73, 0.88]
##      t_varIQR_celsius 1.43 [1.31, 1.61]         1.20      0.70     [0.62, 0.77]
## 
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## 
## Structural Equation Model of psem_fish$model_psem 
## 
## Call:
##   A ~ R + E + VR + MedianT + VarT + TrendT + SkewT
##   VR ~ R + E + MedianT + VarT + TrendT
##   R ~ MedianT + VarT + TrendT
##   E ~ R + MedianT + VarT + TrendT
##   stability ~ R + E + VR + A + (R:MedianT) + MedianT + VarT + TrendT + SkewT
## 
##     AIC
##  6146.839
## 
## ---
## Tests of directed separation:
## 
##     Independ.Claim Test.Type       DF Crit.Value P.Value 
##    R ~ SkewT + ...      coef 456.9584     0.5157  0.4730 
##    E ~ SkewT + ...      coef 306.8676     2.9680  0.0859 
##   VR ~ SkewT + ...      coef 270.2988     2.9794  0.0855 
## 
## --
## Global goodness-of-fit:
## 
## Chi-Squared = NA with P-value = NA and on 3 degrees of freedom
## Fisher's C = 11.325 with P-value = 0.079 and on 6 degrees of freedom
## 
## ---
## Coefficients:
## 
##    Response Predictor Estimate Std.Error       DF Crit.Value P.Value
##           A         R   1.0012    0.0328  62.9350   847.8942  0.0000
##           A         E   0.1136    0.0236 346.7961    22.4552  0.0000
##           A        VR   0.1119    0.0241 496.7346    21.1484  0.0000
##           A   MedianT  -0.0860    0.0299  56.9548     7.9227  0.0067
##           A      VarT   0.0346    0.0296 200.1121     1.3228  0.2515
##           A    TrendT   0.0148    0.0228 280.4936     0.4090  0.5230
##           A     SkewT  -0.0179    0.0273 175.9412     0.4189  0.5183
##          VR         R  -0.5555    0.0617 423.3584    79.4244  0.0000
##          VR         E  -0.2990    0.0403 570.2196    54.5028  0.0000
##          VR   MedianT  -0.3011    0.0602 118.4350    24.6125  0.0000
##          VR      VarT  -0.0370    0.0526 310.4732     0.4841  0.4871
##          VR    TrendT   0.0748    0.0420 448.8656     3.1242  0.0778
##           R   MedianT   0.2288    0.0518 181.7185    19.2135  0.0000
##           R      VarT   0.1965    0.0376 536.5141    27.0185  0.0000
##           R    TrendT  -0.0560    0.0292 575.9680     3.6527  0.0565
##           E         R  -0.4090    0.0625 483.2365    42.1907  0.0000
##           E   MedianT  -0.1701    0.0656 131.6147     6.6184  0.0112
##           E      VarT  -0.1013    0.0556 370.9077     3.2638  0.0716
##           E    TrendT   0.0693    0.0439 497.6634     2.4564  0.1177
##   stability         R  -0.2460    0.1089 558.8370     5.0659  0.0248
##   stability         E  -0.2240    0.0424 562.9324    27.7165  0.0000
##   stability        VR  -0.5537    0.0416 557.8549   176.5603  0.0000
##   stability         A   0.1769    0.0681 542.4500     6.7309  0.0097
##   stability   MedianT  -0.1215    0.0790 199.7818     2.3381  0.1278
##   stability      VarT  -0.1911    0.0586 547.0224    10.5223  0.0013
##   stability    TrendT  -0.0125    0.0433 563.4716     0.0827  0.7738
##   stability     SkewT  -0.1347    0.0586 398.7438     5.2196  0.0229
##   stability R:MedianT  -0.0669    0.0630 569.2542     1.1224  0.2898
##   Std.Estimate    
##         1.0012 ***
##         0.1136 ***
##         0.1119 ***
##        -0.0860  **
##         0.0346    
##         0.0148    
##        -0.0179    
##        -0.5555 ***
##        -0.2990 ***
##        -0.3011 ***
##        -0.0370    
##         0.0748    
##         0.2288 ***
##         0.1965 ***
##        -0.0560    
##        -0.4090 ***
##        -0.1701   *
##        -0.1013    
##         0.0693    
##        -0.2460   *
##        -0.2240 ***
##        -0.5537 ***
##         0.1769  **
##        -0.1215    
##        -0.1911  **
##        -0.0125    
##        -0.1347   *
##        -0.0576    
## 
##   Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05
## 
## ---
## Individual R-squared:
## 
##    Response method Marginal Conditional
##           A   none     0.78        0.78
##          VR   none     0.39        0.50
##           R   none     0.15        0.55
##           E   none     0.27        0.44
##   stability   none     0.24        0.52
## ============ model summary for fish subset ===========
## # Check for Multicollinearity
## 
## Low Correlation
## 
##                  Term  VIF   VIF 95% CI Increased SE Tolerance Tolerance 95% CI
##                     R 3.14 [2.67, 3.75]         1.77      0.32     [0.27, 0.37]
##                     E 1.20 [1.10, 1.40]         1.09      0.83     [0.71, 0.91]
##                    VR 1.27 [1.15, 1.48]         1.13      0.79     [0.68, 0.87]
##                     A 2.51 [2.16, 2.98]         1.59      0.40     [0.34, 0.46]
##         t_med_celsius 1.53 [1.36, 1.78]         1.24      0.65     [0.56, 0.74]
##  t.sens.slope.celsius 1.17 [1.08, 1.38]         1.08      0.85     [0.73, 0.93]
##         t_skw_celsius 1.30 [1.17, 1.51]         1.14      0.77     [0.66, 0.85]
##      t_varIQR_celsius 1.64 [1.45, 1.91]         1.28      0.61     [0.52, 0.69]
## 
  |                                                                            
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## 
## Structural Equation Model of psem_fish$model_psem 
## 
## Call:
##   A ~ R + E + VR + MedianT + VarT + TrendT + SkewT
##   VR ~ R + E + MedianT + VarT + TrendT
##   R ~ MedianT + VarT + TrendT
##   E ~ R + MedianT + VarT + TrendT
##   stability ~ R + E + VR + A + (R:MedianT) + MedianT + VarT + TrendT + SkewT
## 
##     AIC
##  3842.186
## 
## ---
## Tests of directed separation:
## 
##     Independ.Claim Test.Type       DF Crit.Value P.Value 
##    R ~ SkewT + ...      coef 218.4151     0.0025  0.9603 
##    E ~ SkewT + ...      coef 222.4839     0.6325  0.4273 
##   VR ~ SkewT + ...      coef 160.7222     1.9303  0.1666 
## 
## --
## Global goodness-of-fit:
## 
## Chi-Squared = NA with P-value = NA and on 3 degrees of freedom
## Fisher's C = 5.366 with P-value = 0.498 and on 6 degrees of freedom
## 
## ---
## Coefficients:
## 
##    Response Predictor Estimate Std.Error       DF Crit.Value P.Value
##           A         R   0.9888    0.0393  17.6050   474.4369  0.0000
##           A         E   0.1051    0.0294 160.3627    11.9838  0.0007
##           A        VR   0.1186    0.0312 244.7211    13.6091  0.0003
##           A   MedianT  -0.0959    0.0369  36.1582     6.3364  0.0164
##           A      VarT   0.0487    0.0407  71.4778     1.3333  0.2521
##           A    TrendT  -0.0030    0.0303 202.4271     0.0096  0.9219
##           A     SkewT   0.0017    0.0366  86.5560     0.0021  0.9636
##          VR         R  -0.5611    0.0751 309.8607    54.4328  0.0000
##          VR         E  -0.1754    0.0526 328.0494    10.9485  0.0010
##          VR   MedianT  -0.2488    0.0743  83.1989    10.9515  0.0014
##          VR      VarT  -0.0472    0.0729 147.4927     0.4057  0.5251
##          VR    TrendT   0.1521    0.0533 287.9211     7.9813  0.0051
##           R   MedianT   0.2569    0.0616  98.2880    17.0351  0.0001
##           R      VarT   0.2858    0.0559 230.1676    25.5485  0.0000
##           R    TrendT  -0.0549    0.0401 342.5768     1.8492  0.1748
##           E         R  -0.4247    0.0729 350.7145    33.5433  0.0000
##           E   MedianT  -0.1340    0.0878 117.1309     2.2876  0.1331
##           E      VarT  -0.1265    0.0799 247.8168     2.4534  0.1185
##           E    TrendT   0.0248    0.0551 342.9323     0.2007  0.6544
##   stability         R  -0.0912    0.1209 345.8177     0.5641  0.4531
##   stability         E  -0.1287    0.0520 341.0703     6.0766  0.0142
##   stability        VR  -0.5490    0.0505 329.5510   117.5795  0.0000
##   stability         A   0.1312    0.0782 310.1591     2.8026  0.0951
##   stability   MedianT  -0.1981    0.1022 177.9536     3.7111  0.0556
##   stability      VarT  -0.2216    0.0859 333.5485     6.5560  0.0109
##   stability    TrendT   0.0034    0.0538 345.4809     0.0038  0.9506
##   stability     SkewT  -0.0873    0.0818 268.9923     1.1212  0.2906
##   stability R:MedianT  -0.1069    0.0788 343.8199     1.8335  0.1766
##   Std.Estimate    
##         0.9888 ***
##         0.1051 ***
##         0.1186 ***
##        -0.0959   *
##         0.0487    
##        -0.0030    
##         0.0017    
##        -0.5611 ***
##        -0.1754  **
##        -0.2488  **
##        -0.0472    
##         0.1521  **
##         0.2569 ***
##         0.2858 ***
##        -0.0549    
##        -0.4247 ***
##        -0.1340    
##        -0.1265    
##         0.0248    
##        -0.0912    
##        -0.1287   *
##        -0.5490 ***
##         0.1312    
##        -0.1981    
##        -0.2216   *
##         0.0034    
##        -0.0873    
##        -0.0743    
## 
##   Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05
## 
## ---
## Individual R-squared:
## 
##    Response method Marginal Conditional
##           A   none     0.77        0.77
##          VR   none     0.37        0.50
##           R   none     0.22        0.52
##           E   none     0.26        0.56
##   stability   none     0.22        0.64
## ============ model summary for birds ===========
## # Check for Multicollinearity
## 
## Low Correlation
## 
##                  Term  VIF   VIF 95% CI Increased SE Tolerance Tolerance 95% CI
##                     R 1.87 [1.73, 2.04]         1.37      0.53     [0.49, 0.58]
##                     E 1.10 [1.05, 1.19]         1.05      0.91     [0.84, 0.95]
##                    VR 1.91 [1.76, 2.08]         1.38      0.52     [0.48, 0.57]
##                     A 2.14 [1.97, 2.33]         1.46      0.47     [0.43, 0.51]
##         t_med_celsius 1.13 [1.08, 1.22]         1.06      0.88     [0.82, 0.93]
##  t.sens.slope.celsius 1.06 [1.02, 1.17]         1.03      0.95     [0.86, 0.98]
##        t_kurt_celsius 1.19 [1.13, 1.28]         1.09      0.84     [0.78, 0.89]
##      t_varIQR_celsius 1.30 [1.22, 1.40]         1.14      0.77     [0.71, 0.82]
## 
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  |======================================================================| 100%
## 
## Structural Equation Model of psem_birds$model_psem 
## 
## Call:
##   A ~ R + E + VR + MedianT + VarT + TrendT + KurtT
##   VR ~ R + E + MedianT + VarT + TrendT
##   R ~ MedianT + VarT + TrendT
##   E ~ R + MedianT + VarT + TrendT + KurtT
##   stability ~ R + E + VR + A + (R:MedianT) + MedianT + VarT + TrendT + KurtT
## 
##     AIC
##  13988.537
## 
## ---
## Tests of directed separation:
## 
##     Independ.Claim Test.Type       DF Crit.Value P.Value 
##    R ~ KurtT + ...      coef 1229.173      0.334  0.5634 
##   VR ~ KurtT + ...      coef 1074.700      0.048  0.8266 
## 
## --
## Global goodness-of-fit:
## 
## Chi-Squared = NA with P-value = NA and on 2 degrees of freedom
## Fisher's C = 1.528 with P-value = 0.822 and on 4 degrees of freedom
## 
## ---
## Coefficients:
## 
##    Response Predictor Estimate Std.Error        DF Crit.Value P.Value
##           A         R   0.7490    0.0221  447.1684  1134.6897  0.0000
##           A         E   0.1627    0.0211  660.8626    58.5169  0.0000
##           A        VR   0.6054    0.0209 1182.3204   836.5760  0.0000
##           A   MedianT   0.0055    0.0253  163.1374     0.0471  0.8285
##           A      VarT   0.0655    0.0257  813.7156     6.4313  0.0114
##           A    TrendT   0.0117    0.0233  300.0538     0.2495  0.6178
##           A     KurtT   0.0172    0.0227  530.3014     0.5640  0.4530
##          VR         R  -0.3076    0.0321  832.6035    90.6595  0.0000
##          VR         E  -0.2165    0.0299 1060.2572    52.1107  0.0000
##          VR   MedianT  -0.0022    0.0457  228.2758     0.0023  0.9619
##          VR      VarT  -0.0688    0.0338 1035.7142     4.1150  0.0428
##          VR    TrendT  -0.0335    0.0375  599.1077     0.7868  0.3754
##           R   MedianT  -0.0310    0.0516  693.6981     0.3563  0.5507
##           R      VarT   0.0236    0.0291 1238.6214     0.6521  0.4195
##           R    TrendT  -0.0012    0.0345 1230.3185     0.0011  0.9730
##           E         R  -0.0793    0.0312 1233.5632     6.4278  0.0114
##           E   MedianT   0.1267    0.0550  543.4833     5.2528  0.0223
##           E      VarT  -0.0126    0.0343 1237.8231     0.1346  0.7137
##           E    TrendT   0.0754    0.0379 1183.2429     3.9247  0.0478
##           E     KurtT  -0.0769    0.0314 1237.2402     5.9692  0.0147
##   stability         R   0.1315    0.0318 1119.1701    16.9841  0.0000
##   stability         E  -0.0495    0.0225 1102.5970     4.7975  0.0287
##   stability        VR  -0.6952    0.0269 1227.7151   663.7277  0.0000
##   stability         A  -0.1310    0.0275 1219.4755    22.7557  0.0000
##   stability   MedianT  -0.0037    0.0375  263.5502     0.0094  0.9228
##   stability      VarT  -0.0112    0.0266 1136.0895     0.1762  0.6747
##   stability    TrendT   0.0341    0.0275  640.8536     1.5224  0.2177
##   stability     KurtT   0.0189    0.0242 1038.8229     0.6057  0.4366
##   stability R:MedianT   0.0416    0.0229  759.8032     3.2678  0.0710
##   Std.Estimate    
##         0.7490 ***
##         0.1627 ***
##         0.6054 ***
##         0.0055    
##         0.0655   *
##         0.0117    
##         0.0172    
##        -0.3076 ***
##        -0.2165 ***
##        -0.0022    
##        -0.0688   *
##        -0.0335    
##        -0.0310    
##         0.0236    
##        -0.0012    
##        -0.0793   *
##         0.1267   *
##        -0.0126    
##         0.0754   *
##        -0.0769   *
##         0.1315 ***
##        -0.0495   *
##        -0.6952 ***
##        -0.1310 ***
##        -0.0037    
##        -0.0112    
##         0.0341    
##         0.0189    
##         0.0474    
## 
##   Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05
## 
## ---
## Individual R-squared:
## 
##    Response method Marginal Conditional
##           A   none     0.58        0.59
##          VR   none     0.15        0.32
##           R   none     0.00        0.65
##           E   none     0.03        0.58
##   stability   none     0.57        0.65
## ============ model summary for fish ===========
## # Check for Multicollinearity
## 
## Low Correlation
## 
##                  Term  VIF   VIF 95% CI Increased SE Tolerance Tolerance 95% CI
##                     R 3.24 [2.84, 3.72]         1.80      0.31     [0.27, 0.35]
##                     E 1.28 [1.18, 1.43]         1.13      0.78     [0.70, 0.85]
##                    VR 1.31 [1.21, 1.47]         1.15      0.76     [0.68, 0.83]
##                     A 2.59 [2.29, 2.97]         1.61      0.39     [0.34, 0.44]
##         t_med_celsius 1.48 [1.35, 1.67]         1.22      0.67     [0.60, 0.74]
##  t.sens.slope.celsius 1.15 [1.08, 1.30]         1.07      0.87     [0.77, 0.93]
##        t_kurt_celsius 1.29 [1.19, 1.45]         1.14      0.77     [0.69, 0.84]
##      t_varIQR_celsius 1.50 [1.36, 1.69]         1.23      0.67     [0.59, 0.73]
## 
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  |======================================================================| 100%
## 
## Structural Equation Model of psem_fish$model_psem 
## 
## Call:
##   A ~ R + E + VR + MedianT + VarT + TrendT + KurtT
##   VR ~ R + E + MedianT + VarT + TrendT
##   R ~ MedianT + VarT + TrendT
##   E ~ R + MedianT + VarT + TrendT + KurtT
##   stability ~ R + E + VR + A + (R:MedianT) + MedianT + VarT + TrendT + KurtT
## 
##     AIC
##  6048.136
## 
## ---
## Tests of directed separation:
## 
##     Independ.Claim Test.Type       DF Crit.Value P.Value  
##    R ~ KurtT + ...      coef 474.4466     0.8827  0.3479  
##   VR ~ KurtT + ...      coef 293.0998     4.3328  0.0383 *
## 
## --
## Global goodness-of-fit:
## 
## Chi-Squared = 78.585 with P-value = 0 and on 2 degrees of freedom
## Fisher's C = 8.639 with P-value = 0.071 and on 4 degrees of freedom
## 
## ---
## Coefficients:
## 
##    Response Predictor Estimate Std.Error       DF Crit.Value P.Value
##           A         R   1.0784    0.0353  93.1919   867.0076  0.0000
##           A         E   0.1208    0.0234 409.1075    25.9621  0.0000
##           A        VR   0.1204    0.0238 521.8463    25.3079  0.0000
##           A   MedianT  -0.1053    0.0307  56.0372    11.2763  0.0014
##           A      VarT   0.0147    0.0293 171.8530     0.2418  0.6236
##           A    TrendT   0.0198    0.0224 265.2202     0.7606  0.3839
##           A     KurtT   0.0111    0.0253 181.9446     0.1870  0.6659
##          VR         R  -0.5555    0.0617 423.3584    79.4244  0.0000
##          VR         E  -0.2990    0.0403 570.2196    54.5028  0.0000
##          VR   MedianT  -0.3011    0.0602 118.4350    24.6125  0.0000
##          VR      VarT  -0.0370    0.0526 310.4732     0.4841  0.4871
##          VR    TrendT   0.0748    0.0420 448.8656     3.1242  0.0778
##           R   MedianT   0.2288    0.0518 181.7185    19.2135  0.0000
##           R      VarT   0.1965    0.0376 536.5141    27.0185  0.0000
##           R    TrendT  -0.0560    0.0292 575.9680     3.6527  0.0565
##           E         R  -0.4290    0.0662 489.1821    41.2864  0.0000
##           E   MedianT  -0.1931    0.0742 138.3461     6.6402  0.0110
##           E      VarT  -0.1070    0.0605 410.2830     3.0749  0.0803
##           E    TrendT   0.0768    0.0443 490.1647     2.9560  0.0862
##           E     KurtT  -0.0181    0.0528 354.4215     0.1156  0.7340
##   stability         R  -0.2463    0.1196 558.9948     4.2128  0.0406
##   stability         E  -0.2214    0.0430 554.5971    26.3797  0.0000
##   stability        VR  -0.5498    0.0422 547.7665   169.2165  0.0000
##   stability         A   0.1828    0.0710 520.0110     6.6113  0.0104
##   stability   MedianT  -0.1430    0.0787 170.6970     3.2606  0.0727
##   stability      VarT  -0.1992    0.0596 485.6580    11.0336  0.0010
##   stability    TrendT  -0.0150    0.0433 537.6676     0.1184  0.7309
##   stability     KurtT   0.0898    0.0522 430.7731     2.9168  0.0884
##   stability R:MedianT  -0.1102    0.0645 558.9765     2.9105  0.0886
##   Std.Estimate    
##         1.0784 ***
##         0.1208 ***
##         0.1204 ***
##        -0.1053  **
##         0.0147    
##         0.0198    
##         0.0111    
##        -0.5555 ***
##        -0.2990 ***
##        -0.3011 ***
##        -0.0370    
##         0.0748    
##         0.2288 ***
##         0.1965 ***
##        -0.0560    
##        -0.4290 ***
##        -0.1931   *
##        -0.1070    
##         0.0768    
##        -0.0181    
##        -0.2463   *
##        -0.2214 ***
##        -0.5498 ***
##         0.1828   *
##        -0.1430    
##        -0.1992 ***
##        -0.0150    
##         0.0898    
##        -0.0948    
## 
##   Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05
## 
## ---
## Individual R-squared:
## 
##    Response method Marginal Conditional
##           A   none     0.80        0.81
##          VR   none     0.39        0.50
##           R   none     0.15        0.55
##           E   none     0.29        0.45
##   stability   none     0.25        0.49
## ============ model summary for fish subset ===========
## # Check for Multicollinearity
## 
## Low Correlation
## 
##                  Term  VIF   VIF 95% CI Increased SE Tolerance Tolerance 95% CI
##                     R 3.34 [2.83, 4.00]         1.83      0.30     [0.25, 0.35]
##                     E 1.21 [1.11, 1.42]         1.10      0.83     [0.70, 0.90]
##                    VR 1.28 [1.16, 1.49]         1.13      0.78     [0.67, 0.87]
##                     A 2.66 [2.28, 3.17]         1.63      0.38     [0.32, 0.44]
##         t_med_celsius 1.52 [1.35, 1.77]         1.23      0.66     [0.56, 0.74]
##  t.sens.slope.celsius 1.16 [1.07, 1.37]         1.08      0.86     [0.73, 0.94]
##        t_kurt_celsius 1.32 [1.19, 1.54]         1.15      0.76     [0.65, 0.84]
##      t_varIQR_celsius 1.70 [1.49, 1.99]         1.30      0.59     [0.50, 0.67]
## 
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  |                                                                            
  |======================================================================| 100%
## 
## Structural Equation Model of psem_fish$model_psem 
## 
## Call:
##   A ~ R + E + VR + MedianT + VarT + TrendT + KurtT
##   VR ~ R + E + MedianT + VarT + TrendT
##   R ~ MedianT + VarT + TrendT
##   E ~ R + MedianT + VarT + TrendT + KurtT
##   stability ~ R + E + VR + A + (R:MedianT) + MedianT + VarT + TrendT + KurtT
## 
##     AIC
##  3767.796
## 
## ---
## Tests of directed separation:
## 
##     Independ.Claim Test.Type       DF Crit.Value P.Value 
##    R ~ KurtT + ...      coef 247.2314     2.0192  0.1566 
##   VR ~ KurtT + ...      coef 182.3856     2.7137  0.1012 
## 
## --
## Global goodness-of-fit:
## 
## Chi-Squared = 55.646 with P-value = 0 and on 2 degrees of freedom
## Fisher's C = 8.289 with P-value = 0.082 and on 4 degrees of freedom
## 
## ---
## Coefficients:
## 
##    Response Predictor Estimate Std.Error       DF Crit.Value P.Value
##           A         R   1.0407    0.0398  14.1819   503.7682  0.0000
##           A         E   0.1142    0.0287 142.3959    14.7831  0.0002
##           A        VR   0.1295    0.0307 228.4381    16.7192  0.0001
##           A   MedianT  -0.1120    0.0346  27.4854     9.7957  0.0041
##           A      VarT   0.0317    0.0374  40.9766     0.6483  0.4254
##           A    TrendT  -0.0095    0.0288 151.8061     0.1033  0.7484
##           A     KurtT  -0.0055    0.0321  71.2760     0.0274  0.8690
##          VR         R  -0.5611    0.0751 309.8607    54.4328  0.0000
##          VR         E  -0.1754    0.0526 328.0494    10.9485  0.0010
##          VR   MedianT  -0.2488    0.0743  83.1989    10.9515  0.0014
##          VR      VarT  -0.0472    0.0729 147.4927     0.4057  0.5251
##          VR    TrendT   0.1521    0.0533 287.9211     7.9813  0.0051
##           R   MedianT   0.2569    0.0616  98.2880    17.0351  0.0001
##           R      VarT   0.2858    0.0559 230.1676    25.5485  0.0000
##           R    TrendT  -0.0549    0.0401 342.5768     1.8492  0.1748
##           E         R  -0.4413    0.0766 335.3222    32.8430  0.0000
##           E   MedianT  -0.1902    0.0998 140.7310     3.5446  0.0618
##           E      VarT  -0.1707    0.0890 262.2840     3.6034  0.0588
##           E    TrendT   0.0417    0.0560 334.9250     0.5493  0.4591
##           E     KurtT  -0.0880    0.0715 283.2761     1.4858  0.2239
##   stability         R  -0.0513    0.1305 320.9321     0.1533  0.6957
##   stability         E  -0.1169    0.0525 332.6805     4.9057  0.0274
##   stability        VR  -0.5396    0.0509 319.8274   111.7596  0.0000
##   stability         A   0.1177    0.0808 286.8070     2.1163  0.1468
##   stability   MedianT  -0.2691    0.1013 172.9798     6.9598  0.0091
##   stability      VarT  -0.2583    0.0868 302.3396     8.7024  0.0034
##   stability    TrendT  -0.0060    0.0538 336.9948     0.0122  0.9121
##   stability     KurtT  -0.0066    0.0692 315.7991     0.0089  0.9250
##   stability R:MedianT  -0.1391    0.0800 335.7542     3.0082  0.0838
##   Std.Estimate    
##         1.0407 ***
##         0.1142 ***
##         0.1295 ***
##        -0.1120  **
##         0.0317    
##        -0.0095    
##        -0.0055    
##        -0.5611 ***
##        -0.1754  **
##        -0.2488  **
##        -0.0472    
##         0.1521  **
##         0.2569 ***
##         0.2858 ***
##        -0.0549    
##        -0.4413 ***
##        -0.1902    
##        -0.1707    
##         0.0417    
##        -0.0880    
##        -0.0513    
##        -0.1169   *
##        -0.5396 ***
##         0.1177    
##        -0.2691  **
##        -0.2583  **
##        -0.0060    
##        -0.0066    
##        -0.0966    
## 
##   Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05
## 
## ---
## Individual R-squared:
## 
##    Response method Marginal Conditional
##           A   none     0.79        0.79
##          VR   none     0.37        0.50
##           R   none     0.22        0.52
##           E   none     0.28        0.57
##   stability   none     0.23        0.62

5 Discussion